Mind Science

Towards Equations for Brain Dynamics and the Concept of Extended Connectome

The brain is a system at the edge of chaos equipped with nonlinear dynamics and functional energetic landscapes. However, still doubts exist concerning the type of attractors or the trajectories followed by particles in the nervous phase space. Starting from an unusual system governed by differential equations in which a dissipative strange attractor coexists with an invariant conservative torus, we developed a 3D model of brain phase space which has the potential to be operationalized and assessed empirically. We achieved a system displaying both a torus and a strange attractor, depending just on the initial conditions. Further, the system generates a funnel-like attractor equipped with a fractal structure. Changes in three easily detectable brain phase parameters (log frequency, excitatory/inhibitory ratio and fractal slope) lead to modifications in funnel’s breadth or in torus/attractor superimposition: it explains a large repertoire of brain functions and activities, such as sensations/perceptions, memory and self-generated thoughts.

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